I want to know which of the groups will be given higher priority $\ce{-C#CH}$ or $\ce{-C(CH3)3}$ and why. I tried resolving the triple bond to single bonds such that they are phantom atoms. But that gave me a structure in which there are no atoms after the first point of difference. How is this (see image) wrong and if this is correct then isn't it a contradiction? After first point of difference, there are two difference one is nothing v/s $\ce H$ and other is $\ce C$ vs $\ce H$ and both situation seem to contradict in giving their respective group higher priority order.
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I'll point out that there are different schemes for naming compounds. So the answer probably depends on exactly which one that you are using... – MaxW Jul 17 '18 at 15:27
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@marxw for E and Z or R and S we need to first give them priority order. And i want to know which priority is correct and why. – Jasmine Jul 17 '18 at 16:12
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At 2nd point of difference, the phantom carbon is attached to the original carbon and hence its a C-C v/s C-H and its obvious that the former will be given higher priority. Its not right to say that the phantom C is not linked to any atom if its really linked to the original C – Jasmine Jul 18 '18 at 18:27
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For a similar question, see this. – user55119 Jan 27 '23 at 18:09
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From the Wikipedia article on CIP rules.
If an atom A is double-bonded to an atom B, A is treated as being singly bonded to two atoms: B and a "ghost atom" that is a duplicate of B (has the same atomic number) but is not attached to anything except A.
Ghost atoms are attached to resolve the triple/double bond.
So according to CIP rules the two compounds can be resolved as

The pink atoms are ghost carbons
From here we can see that ethyne has a greater preference over isobutyl as after the first point of difference we move over to the next highest order carbon. In ethyne the second carbon is connected to $\ce{C2H}$ whereas the next highest order carbon in isobutyl is connected to $\ce{H3}$.
Glorfindel
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Avyansh Katiyar
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What about ethyne vs -C(CH₃)₂-C(CH₃)₂H ? Does the latter win because they are connected to three hydrogens each, whereas the ghost carbon are not connected to anything? But then what about... I will draw... – Dion Silverman Apr 26 '23 at 15:01
